Symmetry adaptation and two photon spectroscopy of ions in molecular or solid state finite symmetry

14 pages, Tex file. Invited paper at the "V Workshop on Symmetry Methods in Physics", Obninsk, Kaluga region, USSR, 8-12 July 1991Finite symmetry adaptation techniques are applied to the determination of the intensity strength of two-photon transitions for ions with one partly-filled shell nl in crystalline environments of symmetry G. We treat the case of intra- configurational transitions as well as the case of inter-configurational transitions. In both cases, the Wigner-Racah algebra of the chain O(3) > G allows to extract the polarization dependence from the intensity. The reported results are valid for any strength of the crystalline field